Jumps and Motivic Invariants of Semiabelian Jacobians

Abstract We investigate Néron models of Jacobians of singular curves over strictly Henselian discretely valued fields and their behavior under tame base change. For a semiabelian variety, this behavior is governed by a finite sequence of (a priori) real numbers between 0 and 1, called jumps. The jumps are conjectured to be rational, which is known in some cases. The purpose of this paper is to prove this conjecture in the case where the semiabelian variety is the Jacobian of a geometrically integral curve with a push-out singularity. Along the way, we prove the conjecture for algebraic tori which are induced along finite separable extensions and generalize Raynaud’s description of the identity component of the Néron model of the Jacobian of a smooth curve (in terms of the Picard functor of a proper, flat, and regular model) to our situation. The main technical result of this paper is that the exact sequence that decomposes the Jacobian of one of our singular curves into its toric and Abelian parts extends to an exact sequence of Néron models. Previously, only split semiabelian varieties were known to have this property.

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Néron Models and Base Change

10.1007/978-3-319-26638-1 ◽

2016 ◽

Cited By ~ 5

Author(s):

Lars Halvard Halle ◽

Johannes Nicaise

Keyword(s):

Base Change ◽

Neron Models ◽

Néron Models

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Formal completions of Néron models for algebraic tori

Proceedings of the London Mathematical Society ◽

10.1112/plms/pdp039 ◽

2009 ◽

Vol 100 (3) ◽

pp. 607-638 ◽

Cited By ~ 2

Author(s):

Oleg Demchenko ◽

Alexander Gurevich ◽

Xavier Xarles

Keyword(s):

Algebraic Tori ◽

Neron Models ◽

Néron Models

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Variability of the total ozone trend over Europe for the period 1950–2004 derived from reconstructed data

Atmospheric Chemistry and Physics ◽

10.5194/acp-8-2847-2008 ◽

2008 ◽

Vol 8 (11) ◽

pp. 2847-2857 ◽

Cited By ~ 11

Author(s):

J. W. Krzyścin ◽

J. L. Borkowski

Keyword(s):

Total Ozone ◽

A Priori ◽

Smooth Curve ◽

Ozone Level ◽

Svalbard Archipelago ◽

Small Areas ◽

Ozone Data ◽

Curve Fit ◽

Long Term Changes

Abstract. The total ozone data over Europe are available for only few ground-based stations in the pre-satellite era disallowing examination of the spatial trend variability over the whole continent. A need of having gridded ozone data for a trend analysis and input to radiative transfer models stimulated a reconstruction of the daily ozone values since January 1950. Description of the reconstruction model and its validation were a subject of our previous paper. The data base used was built within the objectives of the COST action 726 "Long-term changes and climatology of UV radiation over Europe". Here we focus on trend analyses. The long-term variability of total ozone is discussed using results of a flexible trend model applied to the reconstructed total ozone data for the period 1950–2004. The trend pattern, which comprises both anthropogenic and "natural" component, is not a priori assumed but it comes from a smooth curve fit to the zonal monthly means and monthly grid values. The ozone long-term changes are calculated separately for cold (October–next year April) and warm (May–September) seasons. The confidence intervals for the estimated ozone changes are derived by the block bootstrapping. The statistically significant negative trends are found almost over the whole Europe only in the period 1985–1994. Negative trends up to −3% per decade appeared over small areas in earlier periods when the anthropogenic forcing on the ozone layer was weak . The statistically positive trends are found only during warm seasons 1995–2004 over Svalbard archipelago. The reduction of ozone level in 2004 relative to that before the satellite era is not dramatic, i.e., up to ~−5% and ~−3.5% in the cold and warm subperiod, respectively. Present ozone level is still depleted over many popular resorts in southern Europe and northern Africa. For high latitude regions the trend overturning could be inferred in last decade (1995–2004) as the ozone depleted areas are not found there in 2004 in spite of substantial ozone depletion in the period 1985–1994.

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Crystalline subrepresentations and Neron models

Mathematical Research Letters ◽

10.4310/mrl.2000.v7.n5.a6 ◽

2000 ◽

Vol 7 (5) ◽

pp. 605-614

Author(s):

Minhyong Kim ◽

Susan H. Marshall

Keyword(s):

Neron Models ◽

Néron Models

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Néron models

European Journal of Mathematics ◽

10.1007/s40879-017-0134-8 ◽

2017 ◽

Vol 3 (2) ◽

pp. 171-198

Author(s):

Dino Lorenzini

Keyword(s):

Neron Models ◽

Néron Models

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Néron models and limits of Abel–Jacobi mappings

Compositio Mathematica ◽

10.1112/s0010437x09004400 ◽

2010 ◽

Vol 146 (2) ◽

pp. 288-366 ◽

Cited By ~ 6

Author(s):

Mark Green ◽

Phillip Griffiths ◽

Matt Kerr

Keyword(s):

Normal Function ◽

Motivic Cohomology ◽

Normal Functions ◽

Geometric Setting ◽

Neron Models ◽

A Finite Group ◽

Intermediate Jacobian ◽

Néron Models ◽

Singular Fibre ◽

Finite Singularity

AbstractWe show that the limit of a one-parameter admissible normal function with no singularities lies in a non-classical sub-object of the limiting intermediate Jacobian. Using this, we construct a Hausdorff slit analytic space, with complex Lie group fibres, which ‘graphs’ such normal functions. For singular normal functions, an extension of the sub-object by a finite group leads to the Néron models. When the normal function comes from geometry, that is, a family of algebraic cycles on a semistably degenerating family of varieties, its limit may be interpreted via the Abel–Jacobi map on motivic cohomology of the singular fibre, hence via regulators onK-groups of its substrata. Two examples are worked out in detail, for families of 1-cycles on CY and abelian 3-folds, where this produces interesting arithmetic constraints on such limits. We also show how to compute the finite ‘singularity group’ in the geometric setting.

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